You are correct, for the remote to be working correctly, you should see the light blinking, not see it shine steadily.

I just confirmed this by shining my working Rio and Kenwood remotes into my digital camera and looking through the viewfinder. The LED blinks like a little strobe when I press the button.

In a terrible twist of ironic fate, I was also able to confirm that a remote which shines a steady light is definitely malfunctioning. I dropped the Rio Receiver remote into the hot tub just a few minutes ago, and after cleaning it out, it exhibited exactly the behavior you described: Steady shine even when a button is not being pressed.

/me heads over to the Rio Receiver BBS to post a question about this...